Garcia is an illegal immigrant who crossed into the country about 14 years ago, before her children were born, and the citizenship granted to her children and millions others like them is at the center of a divisive national debate.
Republicans are pushing for congressional hearings to consider changing the nation's 14th Amendment to deny such children the automatic citizenship the Constitution guarantees. They say women like Garcia are taking advantage of a constitutional amendment meant to guarantee the rights of freed slaves, and paint a picture of pregnant women rushing across the border to give birth. A recent Pew Hispanic Center study shows 8 percent of the 4.3 million babies born in the U.S. in 2008 had at least one illegal parent.
A closer examination of the issue shows that the trend is not as dramatic as some immigration opponents have claimed.
Most children of illegal immigrants are born to parents like Garcia who have made the United States their home for years.
Out of 340,000 babies born to illegal immigrants in the United States in 2008, 85 percent of the parents had been in the country for more than a year, and more than half for at least five years, Jeffrey Passel, a senior demographer for Pew, told The Associated Press.
And immigration experts say it's extraordinarily rare for immigrants to come to the U.S. just so they can have babies and get citizenship. In most cases, they come to the U.S. for economic reasons and better hospitals, and end up staying and raising families.
Garcia's husband has been deported and she earns a living selling tamales to other immigrants who live in fear of being deported from the slapdash, impoverished colonias that dot the Texas-Mexico border.
"I think that children aren't at fault for having been born here," Garcia said. "My children always have lived here. They've never gone to another country."
Under current immigration law, Garcia and others like her don't get U.S. citizenship even though their children are Americans.
With an estimated 11.1 million illegal immigrants living in the United States, the issue strikes a chord with many voters - people like retired Air Force nurse and pediatric nurse practitioner Susan Struck, 66, of Double Adobe, Ariz.
"People come over ... and they have babies with U.S. birth certificates, then they go back over the border with that Social Security number, with that birth certificate," and have access to public services, she said at a recent event near the border organized by conservative tea party activists.
Several prominent Republican leaders share Struck's beliefs on the issue. Sen. Lindsey Graham of South Carolina has been a vocal advocate for changing the Constitution, and he helped the issue gain momentum heading into the midterm elections.
"Women have traveled from across the world for the purpose of adding a U.S. passport holder to their family, as far away as China, Turkey and as close as Mexico," said Jon Feere, legal analyst for the Center for Immigration Studies, which advocates for strict immigration laws.
Still, changing the Constitution is highly unlikely, legal scholars say. Measures have been introduced in each two-year congressional session since 2005, but none has made it out of committee. Constitutional changes require approval by two-thirds majorities in both chambers of Congress, an impossibility now because Democrats have the majority in both houses and most oppose such a measure. Even if Republicans gain power in November and legislation is passed, an amendment would still need to be ratified by three-fourths of the states.
To be sure, some pregnant Mexican women do come to the United States. In border cities like Nogales, women have been coming to the U.S. for decades to give birth, although the primary reason is better medical care, Santa Cruz County sheriff Tony Estrada said. Billboards advertising birthing services in Arizona line streets across the border in Nogales, Mexico.
Tucson Medical Center, 115 miles southeast of Phoenix, offers packages designed to provide inclusive care to new mothers. The program draws some residents of the northern Mexican state of Sonora who can afford its upfront costs and already have U.S. visas, spokesman Michael Letson said.
Princeton University demographer Douglas Massey said in 30 years studying Mexican immigration, he's never interviewed a migrant who said they came to the United States just to get citizenship for their children.
"Mexicans do not come to have babies in the United States," said Massey, who blames the tightening of the border in the 1990s for cutting off normal migration of men who used to come to work for a year or two and then go home. "They end up having babies in the United States because men can no longer circulate freely back and forth from homes in Mexico to jobs in the United States and husbands and wives quite understandably want to be together."
More common, he and other experts says, are families stuck with one child who is legal and others who aren't - like Beatriz Gomez, a 35-year-old illegal immigrant who came to Phoenix 11 years ago on a now-expired tourist visa from Arriaga in the Mexican state of Chiapas.
Her 12-year-old daughter was born in Mexico and is here illegally, but her two youngest children, ages 8 and 5, were born in the U.S. and are citizens.
"It's sad," Gomez said of her oldest daughter, who was only 1 when the family came to the United States. "She studies hard, and she won't be able to go to a university like the other two."